Exploring spectral density estimation for spatial linear process with mixing innovations

Abstract

We study the asymptotic properties of the spectral density estimator (a periodogram) of a linear spatial process with alpha mixing innovations. A periodogram is a natural estimate of the spectral density. Under some conditions, a relation between the periodograms of innovations and that of the linear process is established in a spatial case. As the estimator of periodogram is inconsistent, a linear filter is introduced and convergence properties of the obtained smoother periodogram estimator are studied.